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RRQRDecomposition (Commons Math 3.2 API)
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org.apache.commons.math3.linear</FONT>
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Class RRQRDecomposition</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">org.apache.commons.math3.linear.QRDecomposition</A>
      <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.linear.RRQRDecomposition</B>
</PRE>
<HR>
<DL>
<DT><PRE>public class <B>RRQRDecomposition</B><DT>extends <A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</A></DL>
</PRE>

<P>
Calculates the rank-revealing QR-decomposition of a matrix, with column pivoting.
 <p>The rank-revealing QR-decomposition of a matrix A consists of three matrices Q,
 R and P such that AP=QR.  Q is orthogonal (Q<sup>T</sup>Q = I), and R is upper triangular.
 If A is m&times;n, Q is m&times;m and R is m&times;n and P is n&times;n.</p>
 <p>QR decomposition with column pivoting produces a rank-revealing QR
 decomposition and the <A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getRank(double)"><CODE>getRank(double)</CODE></A> method may be used to return the rank of the
 input matrix A.</p>
 <p>This class compute the decomposition using Householder reflectors.</p>
 <p>For efficiency purposes, the decomposition in packed form is transposed.
 This allows inner loop to iterate inside rows, which is much more cache-efficient
 in Java.</p>
 <p>This class is based on the class with similar name from the
 <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
 following changes:</p>
 <ul>
   <li>a <A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getQT()"><CODE>getQT</CODE></A> method has been added,</li>
   <li>the <code>solve</code> and <code>isFullRank</code> methods have been replaced
   by a <A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getSolver()"><CODE>getSolver</CODE></A> method and the equivalent methods
   provided by the returned <A HREF="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><CODE>DecompositionSolver</CODE></A>.</li>
 </ul>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.2</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: RRQRDecomposition.java 1456956 2013-03-15 13:54:20Z luc $</DD>
<DT><B>See Also:</B><DD><a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a>, 
<a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a></DL>
<HR>

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<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix)">RRQRDecomposition</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the QR-decomposition of the given matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)">RRQRDecomposition</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
                  double&nbsp;threshold)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the QR-decomposition of the given matrix.</TD>
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<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#decompose(double[][])">decompose</A></B>(double[][]&nbsp;qrt)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Decompose matrix.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getP()">getP</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.</TD>
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<CODE>&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getRank(double)">getRank</A></B>(double&nbsp;dropThreshold)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Return the effective numerical matrix rank.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getSolver()">getSolver</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get a solver for finding the A &times; X = B solution in least square sense.</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#performHouseholderReflection(int, double[][])">performHouseholderReflection</A></B>(int&nbsp;minor,
                             double[][]&nbsp;qrt)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Perform Householder reflection for a minor A(minor, minor) of A.</TD>
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&nbsp;<A NAME="methods_inherited_from_class_org.apache.commons.math3.linear.QRDecomposition"><!-- --></A>
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<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math3.linear.<A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getH()">getH</A>, <A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getQ()">getQ</A>, <A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getQT()">getQT</A>, <A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getR()">getR</A></CODE></TD>
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<A NAME="RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix)"><!-- --></A><H3>
RRQRDecomposition</H3>
<PRE>
public <B>RRQRDecomposition</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix)</PRE>
<DL>
<DD>Calculates the QR-decomposition of the given matrix.
 The singularity threshold defaults to zero.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>matrix</CODE> - The matrix to decompose.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)"><CODE>RRQRDecomposition(RealMatrix, double)</CODE></A></DL>
</DL>
<HR>

<A NAME="RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)"><!-- --></A><H3>
RRQRDecomposition</H3>
<PRE>
public <B>RRQRDecomposition</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
                         double&nbsp;threshold)</PRE>
<DL>
<DD>Calculates the QR-decomposition of the given matrix.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>matrix</CODE> - The matrix to decompose.<DD><CODE>threshold</CODE> - Singularity threshold.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix)"><CODE>RRQRDecomposition(RealMatrix)</CODE></A></DL>
</DL>

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<A NAME="decompose(double[][])"><!-- --></A><H3>
decompose</H3>
<PRE>
protected void <B>decompose</B>(double[][]&nbsp;qrt)</PRE>
<DL>
<DD>Decompose matrix.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#decompose(double[][])">decompose</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>qrt</CODE> - transposed matrix</DL>
</DD>
</DL>
<HR>

<A NAME="performHouseholderReflection(int, double[][])"><!-- --></A><H3>
performHouseholderReflection</H3>
<PRE>
protected void <B>performHouseholderReflection</B>(int&nbsp;minor,
                                            double[][]&nbsp;qrt)</PRE>
<DL>
<DD>Perform Householder reflection for a minor A(minor, minor) of A.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#performHouseholderReflection(int, double[][])">performHouseholderReflection</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>minor</CODE> - minor index<DD><CODE>qrt</CODE> - transposed matrix</DL>
</DD>
</DL>
<HR>

<A NAME="getP()"><!-- --></A><H3>
getP</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>getP</B>()</PRE>
<DL>
<DD>Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.

 If no pivoting is used in this decomposition then P is equal to the identity matrix.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>a permutation matrix.</DL>
</DD>
</DL>
<HR>

<A NAME="getRank(double)"><!-- --></A><H3>
getRank</H3>
<PRE>
public int <B>getRank</B>(double&nbsp;dropThreshold)</PRE>
<DL>
<DD>Return the effective numerical matrix rank.
 <p>The effective numerical rank is the number of non-negligible
 singular values.</p>
 <p>This implementation looks at Frobenius norms of the sequence of
 bottom right submatrices.  When a large fall in norm is seen,
 the rank is returned. The drop is computed as:</p>
 <pre>
   (thisNorm/lastNorm) * rNorm < dropThreshold
 </pre>
 <p>
 where thisNorm is the Frobenius norm of the current submatrix,
 lastNorm is the Frobenius norm of the previous submatrix,
 rNorm is is the Frobenius norm of the complete matrix
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>dropThreshold</CODE> - threshold triggering rank computation
<DT><B>Returns:</B><DD>effective numerical matrix rank</DL>
</DD>
</DL>
<HR>

<A NAME="getSolver()"><!-- --></A><H3>
getSolver</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</A> <B>getSolver</B>()</PRE>
<DL>
<DD>Get a solver for finding the A &times; X = B solution in least square sense.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getSolver()">getSolver</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>a solver</DL>
</DD>
</DL>
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